a new local binary probabilistic pattern (lbpp) and ...€¦ · a new local binary probabilistic...

A New Local Binary Probabilistic Pattern (LBPP) and Subspace

methods for face recognition

1*Abdellatif Dahmouni,

2Karim El Moutaouakil, and

1Khalid Satori

1LIIAN, Department of Mathematics and computer science

Faculty of Sciences, Dhar-Mahraz Sidi Mohamed Ben Abdellah

B.P 1796 Atlas-Fez 2INSAH, National School of Applied Sciences Al Hoceima

BP 03, Ajdir Al-Hoceima University Mohamed 1

Morocco

[email protected]

[email protected]

[email protected]

Abstract: - In this paper, we present a new model of extraction of local characteristics, named Local Binary

Probabilistic Pattern (LBPP), and based on the Local Binary Pattern (LBP). This model relates to a very

important result of probability theory; it is the large great numbers. In this respect, the distribution of the gray

levels on the areas (homogeneous texture) on a face image follows a law of probability, which is the sum of

several normal laws. This vision allows evaluating the current pixel while basing on the concept of confidence

interval, which permits to overcome some LBP shortcomings, especially the information losses associated to

LBP deterministic nature. We have combined the proposed model with the most known algorithms of the

dimensionality reduction of data analysis in the face recognition field. In order to evaluate our approach,

various experiments are carried out on data bases ORL and YALE. In this context, we made a comparison

between the performances of systems LBP+ACP, LBP+LDA, LBP+2DPCA, LBP+2DLDA, LBPP+ACP,

LBPP+LDA, LBPP+2DPCA and LBPP+2DLDA. The obtained results show the effectiveness of our systems,

in particular for systems LBPP+2DPCA and LBPP+2DLDA. The experimental exactitude observed is of

96.5%.

Key-Words: - LBP, LBPP, PCA, LDA, 2DPCA, 2DLDA, Confidence interval

1 Introduction The face recognition is a biometric modality which

involves several fields of research; it covers many

applications such as biometric systems, computer

security systems, access control systems, and

surveillance systems [24]. Many approaches are

developed for face recognition: Principal

Components Analysis PCA and 2DPCA [1][2],

Linear Discriminate Analysis LDA and 2DLDA

[3][4], Independent Component Analysis ICA [5],

Artificial Neural Networks ANN [6][22][25],

Hidden Markov Models HMM [7][23], Gabor

Wavelets [8], and Local Binary Pattern LBP [11].

The fusion between the dimensionality reduction

methods and the local characteristics extraction

methods is a key stage for face recognition. In this

work, we focus on fusion between the PCA, LDA,

2DPCA, and 2DLDA methods, and some extended

methods of local binary pattern LBP.

The local binary pattern proposed in [9] is a non

parametric operator for texture analysis, and

extended for face recognition [11], by describing the

face like the primitives composition called micro-

patterns; and for other implementations like: face

detection [17], facial expression [18], age evaluation

[19], Gender classification [20], and movement

analysis [21]...

The original LBP uses a neighborhood of (3*3)

pixels, centered on current pixel to calculate its gray

level value. Each of the eight neighboring pixels has

higher or equal value to the current pixel value is

coded by « 1 », the others by « 0 ». The process is

depicted in ‎Fig 1. Where a byte of eight bits is

generated, and then converted into gray level (value

between 0 and 255) by the following mathematical

equation:

(1)

The parameters R and P are respectively the

neighborhood radius and the number of neighboring

pixels around a current pixel.

WSEAS TRANSACTIONS on COMPUTERS Abdellatif Dahmouni, Karim El Moutaouakil, Khalid Satori

E-ISSN: 2224-2872 588 Volume 14, 2015

mailto:[email protected]

The parameters ic and in represent the gray level

values of the current pixel and the neighboring

pixels.

Fig.1 The method of LBP code Calculation

Because of its invariance to the monotonous

lighting changes, and its low calculation complexity,

the LBP became largely used. Several extensions of

LBP are developed:

Ojala proposes a circular neighborhood

(illustrated in Fig 2) to solve the multi-resolution

problems; he noticed that more than 90% of the

texture information present at most two transitions

(01 or 10); for example, 00111111 and 10000011

are uniform patterns. It’s‎ the‎ uniform‎

variety , which reduces the range of the

histogram values to 59 distinct values [10].

Fig.2 Different circular neighborhoods

To overcome the noise consequences Tan

proposes the Local Ternary Pattern LTP, by using a

mode of three bits coding [13]. Ahonen introduces

the Soft-LBP by using fuzzy logic [12], Liao

proposes the multi-blocks MB-LBP, he applies the

LBP descriptor to the rectangular blocks intensities

that consists to substitute the pixels of each blocks

by their average pixel [14]. Jabid proposes the Local

Directional Pattern LDP, which uses the Kirsch

masks as detectors of the maximum information

directions [15]. Bongjin uses the gradient values to

correct the local intensity variations produce along

the edge components, by introducing the Local

Gradient Pattern LGP [16].

The different varieties of LBP suffer from the

loss of information related to the hard thresholding

mode for evaluating a current pixel. What affects

the representation of principal components which

characterize‎a‎face‎(eyes,‎nose,‎mouth…).

In this work, we present a new extension of the

local binary pattern LBP, called local binary

probabilistic pattern LBPP. This model leads to a

very‎ important‎ result‎ of‎ probability‎ theory;‎ it’s‎ the‎

large of great numbers. In this context, the

distribution of the gray levels on a face image

follows a law of probability, which is the sum of

several normal laws. This vision allows evaluating

the current pixel while basing itself on the

confidence interval concept.

Initially, the proposed model is tested with the

spatially enhanced local binary pattern histogram

(eLBPH) presented by Ahonen [11][12], and

combined, in second time, with the most known

algorithms of dimensionality reduction PCA, LDA,

2DPCA and 2DLDA, for face recognition on images

extracted from the databases ORL and YALE.

Also, we compare the performances of the

systems LBP+ (eLBPH, ACP, LDA, 2DPCA and

2DLDA) and LBPP+ (eLBPH, ACP, LDA, 2DPCA

and 2DLDA). The obtained results show the

effectiveness of the proposed approach for face

recognition compared to some existing techniques,

especially for systems LBPP+2DPCA and

LBPP+2DLDA. The observed experimental

exactitude is of 96.5%.

The Following of this paper consists of four

sections followed by a conclusion. The section 2

presents in detail the LBPP descriptor variety based

on the confidence interval. The face recognition

systems based on LBPP are examined in the section

3. The section 4 presents the experimental results

which evaluate the effectiveness of the suggested

approach.

2 Proposed Method: LBPP As many distributions observed in reality, the

distribution in levels of gray in a face follows

approximately a sum of several normal laws. Recall

that the normal law is defined by the

probability density f and the distribution function F

given by:

(2)

(3)

It should be noted this kind of law describes

phenomena which result from the addition of a large

number of independent fluctuations. For areas,

almost homogeneous, exist small variations of

intensity between neighboring pixels, we can

remove these intensities variations by assimilating


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the distribution of the pixels in these areas to a

normal law. Therefore, we have from the mode of

fixed and signed thresholding for LBP [9][11],

absolute and locally adapted for LGP [16], to a

mode of thresholding per confidence interval

depending on the distribution of the pixels in a

neighborhood of a current pixel; see Fig.3 and Fig.4.

Fig.3 Probability density of various confidence

intervals

We propose to generate a confidence

interval , based on statistical moments in a

neighborhood of N=p2 pixels centered on current

pixel. Each of the eight neighboring pixels having a

value located inside the confidence interval is coded

by 1, the others by 0. A byte of eight bits is

generated, and converted into gray level.

Fig.4 Histograms of various areas of LBPP image

2.1 Confidence interval evaluation To evaluate the confidence interval, a random

variable X is associated to the pixel gray level value. The following statistical moments are calculated:

(4)

(5)

(6)

(7)

The normal law is characterized by the symmetry

coefficient null. It appears natural to calculate this

indicator to measure the rapprochement of an

empirical distribution with the normal

law . The evaluation of the fluctuations

related to data dispersion is ensured by constraints

applied on the variation coefficient .

Let us suppose that any variable X fulfilling the

condition:

(8)

Where, β is experimentally determined (β‎ depends‎

of databases ; follows the normal

law , it is a homogeneous neighborhood in

which the probability that X is inside the confidence

interval , is given by:

The normal variable X is almost certainly located

in the interval ; we define a

convergence limit of the normality in the confidence

degree to 99.99% for the interval: therefore . See, Fig.3.

For any variable X not fulfilling (8) one takes:

(10)

Such choices permit to define a limit to radius of

data convergence, and correct the asymmetry and

kurtosis problems. See, Fig.5.

Fig.5 Asymmetry (a) and Kurtosis (b) fluctuations


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2.2 LBPP mathematical formulation The LBPP approach based on the confidence

interval defined in (9) and (10) is given by the

following mathematical formulation:

(11)

The parameter K is defined in (9) and (10).

The parameters R and P are respectively the


pixels that contribute to binary code calculation.

The parameters R’ and P’ are respectively the


pixels that contribute to the statistical moments:

(μ,‎σ,‎δ‎and‎S) calculation.

Contrary to LBP, which is a deterministic model,

our approach considers the face as distributions of

pixels which follow a law of probability. We thus

pass to a probabilistic and statistical description

where the notion of the confidence interval allows

assigning values near 255 at all pixels of almost

homogeneous‎ areas‎ (forehead,‎ cheeks….).‎And‎ the‎

values near 0 at all corners. The nose, eyes and

mouth having of strong curves, will have different

values, will be easily located Fig.4.The LBPP is

robust to local and global intensity variations.

However, in Fig 7(a) where the background and the

foreground together change (global), LBP, and

LBPP codes have the same pattern. By against,

when the background and the foreground separately

change (local), the LBPP code remains invariant,

but LBP code changes Fig 7((b) and (c)).

Fig.6 LBP and LBPP for different changes of the

gray levels intensity: (a) Monotonic change, (b)

Background change, and (c) Foreground change.

3 FACE RECOGNITION SYSTEMS Our approach is tested on different systems.

Initially, we use the histograms information to

establish the feature vector. Afterwards, we use

several dimensionality reduction methods of face

recognition.

3.1 Building eLBPPH Feature Vector Generally, the face recognition approaches based on

LBP descriptor, use the enhanced local binary

pattern histogram (eLBPH) proposed by Ahonen.

To build the eLBPPH feature, the facial image is

divided into R1...Rd not-overlapped rectangular

areas, the histograms of these areas are individually

calculated, and then are together concatenated to

establish a global face description. After, a classifier

based on the histogram matching techniques such as

the popular Chi square statistic (χ2) metric is used

for computation feature vector similarity. See, Fig.7.

(13)

In which and are images histograms,

and is weight for region j.


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Fig.7 The eLBPPH feature vector extracting

For the suggested approach, the analysis of the

histograms of images on ORL and YALE databases;

show that the histogram values are concentrated in

the interval [0-15; 240-255].What reduces the

eLBPPH feature vector. The length of the eLBPPH

is 32*dn2, instead of 59*dn

2 of the uniform LBP, and

256*dn2of the original LBP. Where, dn

2 represent the

size of each block. See, Fig.8

Fig.8 The histograms for LBPP(k=4) images

3.2 Methods of dimensionality reduction To profit from the advantages of the local and

global approaches. The LBPP descriptor is

combined with different dimensionality reduction

algorithms. The dimensionality reduction algorithms

consist in determining an optimal orthogonal basis.

This basis is formed by Eigen vectors of the

covariance matrix constructed starting from the

training images. In contrast, the conventional

algorithms PCA and LDA which transform each

image by a column vector; 2DPCA and 2DLDA

algorithms employ directly the two-dimensional

data to form the covariance matrix. The size of this

matrix is (n,n) instead of (n2,n

2).

Consequently, 2DPCA and 2DLDA have

significant advantages compared to PCA and LDA.

First of all, the face images are less distorted; the

image details are better preserved. In addition it is

easier to evaluate with precision the covariance

matrix, less time is necessary to determine the Eigen

vectors. Moreover, 2DLDA dominates the

singularity problem (the size of the database can

produce of an amendment of covariance not

diagonalizable). The operations of PCA, LDA,

2DPCA and 2DLDA are presented below:

3.2.1 PCA algorithm Stages

The PCA algorithm is presented to the works of

Turk and Pentland. The stages of this algorithm are:

Each image is transformed into a vector

column of m*n size.

The average face of the set is defined by:

(14)

The data set is adjusted to the average with the

following formula:

(15)

The covariance matrix who estimates the dispersion

of all features vectors at their average is defined by:

(16)

The Eigen-vectors of C, corresponding to Eigen-

values are computed by using: Sort the Eigen-vectors according to their

corresponding Eigen-values.

Finally, each testing image is projected in the

training Eigen-space. The images classification is

ensured by the Euclidean distance:

(17)

Suppose that, one has:

(18)

The reduction of the big-size matrix C is reduced

to the reduction of the matrix L much smaller. To

find the Eigen-vectors of C it is enough to multiply

by A the Eigen-vectors of L. The maximum of

information is contained in the first Eigen-values.


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The optimal basis of projection is formed by K

better Eigen-vectors associated to K greater Eigen-

values.

3.2.2 LDA algorithm Stages

The LDA algorithm is presented to the works of

Belhumeur.al. Like the PCA, the stages of LDA

algorithm are:

The average per class is defined by:

(19)

The images for each class are adjusted to their

average:

(20)

Then we calculate the intra-class dispersion matrix

Sw, and inter-class dispersion matrix Sb:

(21)

(22)

The parameter p is total number of class.

The parameter qi is number images in the class Ci

The optimal projection W, which maximizes the

intra class dispersion, and minimizes the interclass

dispersion, must check the following Eigen-values

equation:

(23)

Thus, the projection of an image is:

The classification is ensured with the Euclidean

distance:

(24)

3.2.3 2DPCA algorithm Stages

The 2DPCA method, proposed by Yang.al is based

on the PCA algorithm.

The idea of this method is to project a matrix (m,n)

via a linear transformation such as:

(25)

Where: is known as principal component

vector of dimension (n,1), and is the vector

projection of dimension (m,1). For M images of

training the covariance matrix of size (n, n) is

computed as:

(26)

Where: ψmean is the average matrix of the M

training images (14). The optimal projection basis Ropt=[R1,…,Rg],

obtained by maximization of generalized variance

criterion: J(R)=RTCR, is composed by the first

Eigenvectors corresponding to g greater Eigen

values of the covariance matrix C.

Then we obtain for each image Γ(m,n), a

characteristic matrix Y(m,g)=[Y1,…,Yg], whose

components Y=ΓRopt.

Finally, the similarity between the test image

Ytest and training image Ytrain is measured by the

distance: d=argmin ||Ytest-Ytrain ||.

3.2.4 2DLDA algorithm Stages

Inspired by 2DPCA, Visani.al extended the LDA

algorithm to two-dimensional LDA (2DLDA).

Suppose that images are separate to p-class of q-

images, one appointed as:

The average image of iéme

class :

(27)

The intra-class dispersion matrix Sw

(28)

The inter-class dispersion matrix Sb

(29)

The optimal projection basis Ropt=[R1,…,Rg],

obtained by maximization of Fisher’s criterion:

J(R)=RT R/R

T R, is composed by the first

Eigenvectors corresponding to g greater Eigen

values of the Sw-1

Sb matrix. Then we obtain for each

image Γ(m,n), a characteristic matrix Y(m,g)=[Y1,..,Yg],

whose components Y=ΓRopt

Finally, the similarity between the test image Ytest

and training image Ytrain is measured by the distance:

d=argmin ||Ytest-Ytrain ||.

4 Experimentations To optimize the recognition rate, we propose the

following strategy:

Initially, we use the Ahonen method who

measure the images similarity based on the distance

between histograms.

Secondly, we use the obtained image from LBPP

to direct input of algorithms PCA, LDA, 2DPCA

and 2DLDA.


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To evaluate the performances of the proposed

approach, we have used the databases ORL and

YALE.

To harmonize the gray levels distribution of each

image, one pre-treatment with histogram

equalization is necessary.

Fig.9 Diagram block of approach steps

The ORL database is made of 40 subjects having

each one 10 different views [26]; the images in gray

levels have the same size (92x112) pixels. Some

images were taken at different times, containing

variations of lighting, facial expressions, and details

of the face.

The YALE database is made up of 165 images of

15 subjects representing 11 conditions of lighting,

pose and facial expressions of size (320x243) [27],

centered and scaled to size (112x92) pixels.

As it is shown, in the Fig 3, formed by images

respectively obtained by application of LBP, LBPP

(k=1), LBPP (k=2), LBPP (k=3) and LBPP (k=4).

The pixels of the almost homogeneous areas, and

the pixels of the peaks areas are perfectly separate in

the case of LBPP (k>2).

Fig.10 ORL image obtained by LBP and LBPP(k)

Fig.11 YALE image obtained by LBP and LBPP

4.1 Results of eLBPPH approach Table2 shows the results to eLBPPH applied on

ORL database. To reduce the values of histogram is

a widely justified hypothesis.

Table 1 Rate recognition eLBPPH on ORL

4.2 PCA, LDA, 2DPCA, 2DLDA and LBPP

hybrids Methods To evaluate the performances of the proposed approach, we use the obtained image from to direct input of algorithms PCA, LDA, 2DPCA and 2DLDA.

Initially, we compare the performances (rate and

time recognition) of 2DPCA, 2DLDA and PCA in

terms of rate and time recognition for different

dimensions of Eigen-space projection, for a number

of 5 training images per class of ORL and YALE

databases.

Table 2 Rate and Time recognition for different

Eigen-space dimensions on database ORL

Tables 2 and 3, shows that LBPP+2DPCA and

LBPP+2DLDA algorithms reach their maximum

rate for a small Eigen-base size:

On ORL database:

LBPP+2DPCA: (dim=8; rate=96, 5; time=7, 59) and

LBPP+2DLDA: (dim=8; rate=96, 5; time=9, 48),

differently to LBPP+PCA: (dim=18; rate =87,5;

time = 10, 93).

Dimension of Eigen-

base 4 8 12 16 20

Rate

(%)

LBPP+PCA 57 78,5 85,5 86,5 87,5

LBPP+2DPCA 95 96,5 95 95 94

LBPP+2DLDA 95,5 96,5 96,5 96 95,5

Time

(ms)

LBPP+PCA 10,92 10,78 10,82 10,84 10,93

LBPP+2DPCA 6,34 7,59 9,17 10,44 11,95

LBPP+2DLDA 7,99 9,48 11,19 12,16 13,8

Dimension LBP

LBPP

K=2

LBPP

K=3

LBPP

K=4

Rate

(%)

[0-15,240-255] 90 96 95,5 95,5

[0-255] 92,5 94,5 94 94

Time

(ms)

[0-15,240-255] 59 59 58 58

[0-255] 388 365 364 364


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On Yale database:

LBPP+2DPCA: (dim=4;rate=95,56 ; time=1,95) and

LBPP+2DLDA: (dim=4;rate=96,67; time=2,58),

differently to LBPP+PCA: (dim=12; rate =91,11;

time = 2,84).

Table 3 Rate and Time recognition for different

Eigen-space dimensions on database YALE

We compare the performances of hybridizations

of 2DPCA, 2DLDA, PCA and LDA with LBP and

LBPP (k):

ORL database: for a random set of 5 training

images and 5 testing images per class, and for

optimal base of projection; the top results, illustrated

in Table 4, show that the association of algorithms

(2DPCA, 2DLDA and LBPP (k>2)) gives the best

recognition rate (2DPCA (96, 5), 2DLDA (96,5)).

Table 4 Recognition rate for various LBPP methods

on ORL database

YALE database: for a random set of 5 training

images and 6 testing images per class, and for

optimal base of projection, the top results illustrated

in table 5 show that the association of algorithms

(2DPCA, 2DLDA and LBPP (k>2)) gives the best

recognition rate (2DPCA (96, 67), 2DLDA (93,

33)).

Table 5 Recognition rate for various LBPP methods

on YALE database

We compared the (2DPCA, 2DLDA and LBPP

(k=4)) algorithms with other methods including

Eigen-face, Fisher- face, ICA, 2DPCA and 2DLDA.

The strategy of comparison uses 5 training images

and 5 testing images of each class of database ORL;

the experimental results are illustrated in table4.

Table 6 Comparison with various methods of face

recognition on ORL

The Figures 13 and 14, expose the recognition

rates for different number of training images from

the ORL and Yale databases. The number of

erroneous testing images depends on the training

images number, on used database, on global

methods selected, and on the LBPP confidence

interval size.

Fig.12 Recognition rate with 2DPCA, 2DLDA,

LBP and LBPP(k=2 and k=4) on ORL data

Dimension of Eigen-

base 4 8 12 14 15

Rate

(%)

LBPP+PCA 66,67 85,56 91,11 91,11 91,11

LBPP+2DPCA 95,56 95,56 94,44 94,44 92,22

LBPP+2DLDA 96,67 94,44 94,44 93,33 93,33

Time

(ms)

LBPP+PCA 2,83 2,84 2,84 2,87 2,89

LBPP+2DPCA 1,95 2,18 2,44 2,5 2,59

LBPP+2DLDA 2,58 2,88 3,18 3,42 3,41

ORL PCA LDA 2DPCA 2DLDA

LBP 70% 82,5% 88% 90,5%

LBPP K=1 88% 88,5% 95% 95,5%

LBPP K=2 88,5% 91% 96% 96%

LBPP K=3 87,5% 91% 96,5% 96,5%

LBPP K=4 87,5% 91% 96,5% 96,5%

YALE PCA LDA 2DPCA 2DLDA

LBP 75,56

% 91,11% 90% 91,11%

LBPP K=1

(K=1

94,44

% 93,33% 94,44% 95,56%

LBPP K=2 91,11

% 93,33% 95,56% 96,67%

LBPP K=3 91,11

% 93,33% 95,56% 96,67%

LBPP K=4 91,11

% 93,33% 95,56% 96,67%

Methods Recognition rate

PCA[2] 93,50%

LDA[4] 91,50%

ICA[2] 85,00%

2DPCA[2] 96,00%

2DLDA[4] 92,50%

2DPCA+LBPP(k=4) 96,5%

2DLDA+LBPP(k=4) 96,5%


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Fig.13 Recognition rate with 2DPCA, 2DLDA,

LBP and LBPP(k=2 and k=4) on YALE data

5 Conclusion In this paper, we have proposed a new model for

local characteristics extraction, named LBPP. This

probabilistic LBP variety is based on the idea that

the face pixels distribution follows a probability

law. The normality test estimates the proximity of

this low with the sum normal laws. This vision

minimizes the specific variance to each face by

separating the homogeneous areas from the peaks

areas. The covariance matrix of sub-space methods

is simplified; the margin of histogram values is

reduced; the execution time is improved. It is

possible to replace the x2 metric with the Euclidean

distance in the Ahonen method.

The obtained results by the face recognition system

based on fusion the LBPP with 2DPCA and 2DLDA

methods, prove that the approach based on the

LBPP is robust that based on LBP. The suggested

system reach their best performances for the

confidence interval of k>2.In the future, we will

continue us search in the face recognition field.

Then we will pass to face detection and face

localization fields, in order to lead at robust

biometric system. We would like to implement this

concept to various LBP-varieties, and to merge them

with artificial intelligence and frequency

approaches.

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